CONSTRUCTION OF SMOOTH MORPHISMS ON VARIETIES OF PROJECTIVE COMPLEXES AND DEGENERATION ON DECOMPOSITION OF POLYDULES

• Main Author: (NIM: 30112014), DARMAJID
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/21578
• Institution: Institut Teknologi Bandung

This dissertation deals with varieties of complexes of projective representations with fixed ranks and varieties of polydules with fixed dimensions in homology. There are two main contributions of this dissertation. First, the construction a variety together with two morphisms which enables the study of relation between the variety of projective complexes and the variety of representations of quiver. Second, the construction of degeneration in decomposition of polydules by generalizing some existing results in literature from the module category and projective complex category to polydule category. <br /> <br /> The first main result is the construction a variety Y which contains both of variety of projective complexes and variety of representations of quiver together with two <br /> <br /> morphisms from Y to variety of projective complexes and to variety of representations of quiver. These morphisms are smooth with irreducible fibers. The second main result is the construction of degeneration on decomposition of polydules which generalize the degeneration on decomposition of modules and of projective complexes. <br /> <br /> In this dissertation we also derive some properties about the open condition of some algebraic structure. These properties are the open condition on the set of homomorphism of vector spaces, on the set of chain complexes of vector spaces, and on variety of representations of quiver.